Home  About us  Contact
 

Non-unique Solutions (non-unique + solution)

Distribution by Scientific Domains
Engineering60%

Selected Abstracts

Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002
J. T. Chen
Abstract For a plane elasticity problem, the boundary integral equation approach has been shown to yield a non-unique solution when geometry size is equal to a degenerate scale. In this paper, the degenerate scale problem in the boundary element method (BEM) is analytically studied using the method of stress function. For the elliptic domain problem, the numerical difficulty of the degenerate scale can be solved by using the hypersingular formulation instead of using the singular formulation in the dual BEM. A simple example is shown to demonstrate the failure using the singular integral equations of dual BEM. It is found that the degenerate scale also depends on the Poisson's ratio. By employing the hypersingular formulation in the dual BEM, no degenerate scale occurs since a zero eigenvalue is not embedded in the influence matrix for any case. Copyright © 2002 John Wiley & Sons, Ltd. [source]

GEOLOGICAL INTERPRETATION OF WELL TEST ANALYSIS: A CASE STUDY FROM A FLUVIAL RESERVOIR IN THE GULF OF THAILAND

JOURNAL OF PETROLEUM GEOLOGY, Issue 1 2003
S. Y. Zheng
One problem with the inversion of transient well test data is that it can yield a non-unique solution. The uncertainty resulting from this type of approach can only be resolved by considering information from another source such as geology. Geological information will help to define the interpretation model which will ensure the correct analysis of the well test data. The results of well test analyses are of little value to reservoir characterisation and modelling unless they can be explained from a geological point of view. This last step is what we refer to here as geological interpretation. Other sources of information which can help with well test analyses come from seismic surveys and petrophysics. Modern well test interpretation therefore consists of two major steps: analysis of the well test data; and interpretation of the results. In detail, this should include the following: 1definition of an interpretation model , this requires the integration of geological, seismic and petrophysical data with transient pressure data 2analysis of the well test data based on the interpretation model defined 3geological interpretation of the results, which is necessary in order to explain or give meaning to the results. In this paper, we present a case study from a fluvial gas reservoir in the Gulf of Thailand which demonstrates these procedures. In the context of a defined geological environment, a transient pressure test has been fully analysed. Newly-developed software based on the finite element method has been used to forward model the test scenarios. This allowed the results of seismic and petrophysical analyses to be integrated into the well test model. This case study illustrates the integrated use of geological, petrophysical, well test and seismic attribute data in defining a reservoir model which respects both the reservoir geometry at some distance from the well location and also the reservoir's heterogeneity. We focus on a particular well in the Pattani Basin at which conventional well test analyses have been conducted. By considering the results of these analyses, forward modelling was carried out in which the drainage area was "cut" out of the structural map defined by seismic interpretation; also, the formation's internal heterogeneity was modelled according to well logs and petrophysical analyses. Finally, analytical and simulation results were compared with the transient pressure data. We conclude that the integration of geological, seismic, petrophysical and well test data greatly reduced uncertainties in well test interpretation. The consistency of the results and the fact that they satisfied all the relevant disciplines meant that much more confidence could be given to their interpretation. [source]

On double shearing in frictional materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2007
J. A. M. Teunissen
Abstract This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non-coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro-mechanical and macro-mechanical formulation. The stress,dilatancy theory in the model combines the mechanical behaviour on both scales. It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non-coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity. The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non-coaxial models give non-unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Symmetric Galerkin BEM for multi-connected bodies

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2001
J. J. Pérez-Gavilán
In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Size-broadening anisotropy in whole powder pattern fitting.

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2008
Application to zinc oxide, interpretation of the apparent crystallites in terms of physical models
A new anisotropic size-broadening model based on a spherical-harmonics representation allowing determination of both volume- and area-averaged apparent crystallites and convenient for implementation into Rietveld programs is described. The model effectiveness is demonstrated on a ZnO powder pattern exhibiting strongly anisotropic size broadening and pronounced super-Lorentzian peak shapes. Moreover, it is shown how the apparent crystallites can be interpreted in terms of physical models by using ellipsoidal and cylindrical crystallites with lognormal size distributions. This interpretation is critically assessed and it is argued that both simplified physical models and a priori complementary information (obtained by transmission electron microscopy, for instance) are often needed to avoid unstable and non-unique solutions. [source]